Average Error: 2.1 → 2.2
Time: 3.7s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.61915478997706628 \cdot 10^{-19} \lor \neg \left(t \le -5.91953219351352042 \cdot 10^{-264}\right):\\ \;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.61915478997706628 \cdot 10^{-19} \lor \neg \left(t \le -5.91953219351352042 \cdot 10^{-264}\right):\\
\;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\

\end{array}
double f(double x, double y, double z, double t) {
        double r537003 = x;
        double r537004 = y;
        double r537005 = r537003 / r537004;
        double r537006 = z;
        double r537007 = t;
        double r537008 = r537006 - r537007;
        double r537009 = r537005 * r537008;
        double r537010 = r537009 + r537007;
        return r537010;
}
↓
double f(double x, double y, double z, double t) {
        double r537011 = t;
        double r537012 = -2.6191547899770663e-19;
        bool r537013 = r537011 <= r537012;
        double r537014 = -5.91953219351352e-264;
        bool r537015 = r537011 <= r537014;
        double r537016 = !r537015;
        bool r537017 = r537013 || r537016;
        double r537018 = x;
        double r537019 = y;
        double r537020 = r537018 / r537019;
        double r537021 = z;
        double r537022 = r537020 * r537021;
        double r537023 = -r537011;
        double r537024 = r537020 * r537023;
        double r537025 = r537022 + r537024;
        double r537026 = r537025 + r537011;
        double r537027 = r537021 - r537011;
        double r537028 = r537018 * r537027;
        double r537029 = r537028 / r537019;
        double r537030 = r537029 + r537011;
        double r537031 = r537017 ? r537026 : r537030;
        return r537031;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.1
Target2.5
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.6191547899770663e-19 or -5.91953219351352e-264 < t

    1. Initial program 1.6

      \[\frac{x}{y} \cdot \left(z - t\right) + t\]
    2. Using strategy rm

    3. Applied sub-neg1.6

      \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(z + \left(-t\right)\right)} + t\]

    4. Applied distribute-lft-in1.6

      \[\leadsto \color{blue}{\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right)} + t\]

    if -2.6191547899770663e-19 < t < -5.91953219351352e-264

    1. Initial program 3.7

      \[\frac{x}{y} \cdot \left(z - t\right) + t\]
    2. Using strategy rm

    3. Applied associate-*l/4.4

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.61915478997706628 \cdot 10^{-19} \lor \neg \left(t \le -5.91953219351352042 \cdot 10^{-264}\right):\\ \;\;\;\;\left(\frac{x}{y} \cdot z + \frac{x}{y} \cdot \left(-t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

  (+ (* (/ x y) (- z t)) t))